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We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.

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Preparation of thin films by dissolving polymers in a common solvent followed by evaporation of the solvent has become a routine processing procedure. However, modeling of thin film formation in an evaporating solvent has been challenging due to a need to simulate processes at multiple length and time scales. In this work, we present a methodology based on the principles of linear non-equilibrium thermodynamics, which allows systematic study of various effects such as the changes in the solvent properties due to phase transformation from liquid to vapor and polymer thermodynamics resulting from such solvent transformations. The methodology allows for the derivation of evaporative flux and boundary conditions near each surface for simulations of systems close to the equilibrium. We apply it to study thin film microstructural evolution in phase segregating polymer blends dissolved in a common volatile solvent and deposited on a planar substrate. Effects of the evaporation rates, interactions of the polymers with the underlying substrate and concentration dependent mobilities on the kinetics of thin film formation are studied.

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In this paper, we extend the 3D multispecies diffuse-interface model of the tumor growth, which was derived in Wise et al. (Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524-543), and incorporate the effect of a stiff membrane to model tumor growth in a confined microenvironment. We then develop accurate and efficient numerical methods to solve the model. When the membrane is endowed with a surface energy, the model is variational, and the numerical scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is demonstrably shown to be energy stable. Namely, in the absence of cell proliferation and death, the discrete energy is a nonincreasing function of time for any time and space steps. When a simplified model of membrane elastic energy is used, the resulting model is derived analogously to the surface energy case. However, the elastic energy model is actually nonvariational because certain coupling terms are neglected. Nevertheless, a very stable numerical scheme is developed following the strategy used in the surface energy case. 2D and 3D simulations are performed that demonstrate the accuracy of the algorithm and illustrate the shape instabilities and nonlinear effects of membrane elastic forces that may resist or enhance growth of the tumor. Compared with the standard Crank-Nicholson method, the time step can be up to 25 times larger using the new approach.

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A 66-year-old man with a history of heart transplant for idiopathic dilated cardiomyopathy presented with progressive bone pain and myalgias. He has been on voriconazole for a pulmonary Aspergillus infection for 9 months. He had an elevated alkaline phosphatase of 280. There is no history of rheumatologic disease. Drug-induced periostitis has recently been reported in patients on long-term voriconazole therapy after lung transplantation for prophylaxis and treatment of Aspergillus infection. This case demonstrates the same phenomenon in a heart transplant patient. This patient's symptoms improved after discontinuation of voriconazole.

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We extend the diffuse interface model developed in Wise et al. (2008) to study nonlinear tumor growth in 3-D. Extensions include the tracking of multiple viable cell species populations through a continuum diffuse-interface method, onset and aging of discrete tumor vessels through angiogenesis, and incorporation of individual cell movement using a hybrid continuum-discrete approach. We investigate disease progression as a function of cellular-scale parameters such as proliferation and oxygen/nutrient uptake rates. We find that heterogeneity in the physiologically complex tumor microenvironment, caused by non-uniform distribution of oxygen, cell nutrients, and metabolites, as well as phenotypic changes affecting cellular-scale parameters, can be quantitatively linked to the tumor macro-scale as a mechanism that promotes morphological instability. This instability leads to invasion through tumor infiltration of surrounding healthy tissue. Models that employ a biologically founded, multiscale approach, as illustrated in this work, could help to quantitatively link the critical effect of heterogeneity in the tumor microenvironment with clinically observed tumor growth and invasion. Using patient tumor-specific parameter values, this may provide a predictive tool to characterize the complex in vivo tumor physiological characteristics and clinical response, and thus lead to improved treatment modalities and prognosis.

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PURPOSE: To determine the positive predictive value (PPV) for polyps detected at CT colonography (CTC). METHODS: Assessment of 739 colorectal lesions >or=6 mm detected prospectively at CTC screening in 479 patients was performed. By-polyp PPV was analyzed according to small (6-9 mm) versus large (>or=10 mm) size; morphology (sessile/pedunculated/flat); diagnostic confidence level (3 = most confident, 1 = least confident); and histology. By-patient PPV was analyzed at various polyp size thresholds. RESULTS: By-polyp PPV for CTC-detected lesions >or=6 mm, 6-9 mm, and >or=10 mm was 91.6% (677/739), 90.1% (410/451), and 92.7% (267/288), respectively (p = 0.4). By-polyp PPV according to sessile, pedunculated, flat, and mass-like morphology was 92.5% (441/477), 96.5% (139/144), 77.7% (73/94), and 97.6% (40/41), respectively (p < 0.0001 for flat versus polypoid morphology). By-polyp PPV according to diagnostic confidence level was 94.7% (554/585) for highest (= level 3), 83.5% (106/127) for intermediate (= level 2), and 63.0% (17/27) for lowest (= level 1) confidence (p < 0.0001 for levels-2/3 versus level-1). By-patient PPV at 6-mm, 8-mm, 10-mm, and 30-mm polyp size thresholds was 92.3% (442/479), 93.0% (306/329), 93.1% (228/245), and 97.4% (38/39), respectively. CONCLUSION: The overall per-polyp and per-patient PPV for lesions >or=6 mm was 92% for CTC screening. Increased diagnostic confidence and polypoid (non-flat) morphology correlated with a higher PPV, whereas small versus large polyp size had very little effect.

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Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A wealth of qualitative empirical evidence links disease progression with tumor morphology, histopathology, invasion, and associated molecular phenomena. However, the quantitative contribution of each of the known parameters in this progression remains elusive. Mathematical modeling can provide the capability to quantify the connection between variables governing growth, prognosis, and treatment outcome. By quantifying the link between the tumor boundary morphology and the invasive phenotype, this work provides a quantitative tool for the study of tumor progression and diagnostic/prognostic applications. This establishes a framework for monitoring system perturbation towards development of therapeutic strategies and correlation to clinical outcome for prognosis.

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We develop a thermodynamically consistent mixture model for avascular solid tumor growth which takes into account the effects of cell-to-cell adhesion, and taxis inducing chemical and molecular species. The mixture model is well-posed and the governing equations are of Cahn-Hilliard type. When there are only two phases, our asymptotic analysis shows that earlier single-phase models may be recovered as limiting cases of a two-phase model. To solve the governing equations, we develop a numerical algorithm based on an adaptive Cartesian block-structured mesh refinement scheme. A centered-difference approximation is used for the space discretization so that the scheme is second order accurate in space. An implicit discretization in time is used which results in nonlinear equations at implicit time levels. We further employ a gradient stable discretization scheme so that the nonlinear equations are solvable for very large time steps. To solve those equations we use a nonlinear multilevel/multigrid method which is of an optimal order O(N) where N is the number of grid points. Spherically symmetric and fully two dimensional nonlinear numerical simulations are performed. We investigate tumor evolution in nutrient-rich and nutrient-poor tissues. A number of important results have been uncovered. For example, we demonstrate that the tumor may suffer from taxis-driven fingering instabilities which are most dramatic when cell proliferation is low, as predicted by linear stability theory. This is also observed in experiments. This work shows that taxis may play a role in tumor invasion and that when nutrient plays the role of a chemoattractant, the diffusional instability is exacerbated by nutrient gradients. Accordingly, we believe this model is capable of describing complex invasive patterns observed in experiments.

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PURPOSE: To determine if overhead-throwing athletes with internal impingement pain and internal rotation deficit have thickening of the posterior inferior labrocapsular complex on MR arthrogram images. MATERIALS AND METHODS: This study was approved and a waiver of consent granted by our institutional review board. Twenty-six overhead-throwing athletes with internal impingement pain and internal rotation deficit, and 26 controls who had undergone MR arthrograms, were retrospectively examined. The MR studies were combined and read in a blind fashion. On an axial image through the posteroinferior glenoid rim, the readers measured the labral length, capsule-labrum length, and the posterior recess angle. A t-test was used to determine statistical significance. RESULTS: The mean labral length was 4.9 mm [standard deviation (SD) 1.4 mm] for the controls, and 6.4 mm (SD 1.6 mm) for the athletes (P = 0.001). The mean capsule-labrum length was 5.4 mm (SD 2.1 mm) for the controls, and 8.8 mm (SD 2.9 mm) for the athletes (P < 0.001). The mean posterior recess angle measured 65 degrees (SD 27 degrees) for the controls and 94 degrees (SD 38 degrees) for the athletes (P = 0.002). CONCLUSIONS: Overhead-throwing athletes with internal impingement pain and internal rotation deficit tend to have a thicker labrum and a shallower capsular recess in the posterior inferior shoulder joint than do non-overhead-throwing athletes. In many, the posteroinferior capsule is also thickened. These MR findings should alert the radiologist to closely inspect the posterior cuff and posterosuperior labrum for the tears associated with internal impingement.

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